Answer:
[tex]PO=86.2\\ OM=23.8\\[/tex]
Step-by-step explanation:
To preface, your figure is going to be a line segment, with [tex]O[/tex] as your midpoint, in between points [tex]P[/tex] & [tex]M.[/tex]
With that being said:
[tex]PO+OM=PM[/tex]
Identify your values:
[tex]PO=7y+12\\OM=3y-8\\PM=110[/tex]
Substitute the values into the first equation:
[tex]7y+12+3y-8=110[/tex]
Combine like terms:
[tex]10y+4=110[/tex]
Subtract [tex]4[/tex] from both sides of the equation:
[tex]10y=106[/tex]
Divide by the coefficient of [tex]y[/tex], which is [tex]10[/tex]:
[tex]y=10.6[/tex]
Substitute [tex]10.6[/tex] for [tex]y[/tex] in segments [tex]PO[/tex] & [tex]OM[/tex]:
[tex]PO=7(10.6)+12[/tex]
[tex]OM=3(10.6)-8[/tex]
[tex]PO=74.2+12[/tex]
[tex]OM=31.8-8[/tex]
Solve:
[tex]PO=86.2[/tex]
[tex]OM=23.8[/tex]
Check your answers by substituting:
[tex]PO+OM=PM[/tex]
[tex]86.2+23.8=110[/tex]
